The five-pointed star is the most revered symbol among all the peoples of the world at all times. Her images were discovered at the very beginning of civilization, when writing was not yet invented.
The very first image of a five-pointed star found by archaeologists dates back to 3500 BC. It was captured on an clay tablet found during excavations of the Sumerian city of Uruk.
The star symbol was popular in Ancient Egypt and Babylon. It was revered by the ancient Romans and Greeks, considering the five-pointed star a symbol of the cycle in nature. The Greeks associated the five corners of the star with the five elements of which our world was created - earth, water, air, fire and ether.
The five-pointed star is an attribute of emblems and flags of many modern states and is present on military insignia.
But to draw this plain figure is not as easy as it might seem at first glance.
How to draw a five-pointed star without taking your pencil from paper
The great Greek thinker and mathematician Pythagoras called the five-pointed star mathematical perfection. Indeed, this complex figure can be drawn in one broken line, without tearing the pencil from a sheet of paper and returning at the end to the same starting point from which the drawing was started.
Here she is, a complex and simple at first glance figure - a five-pointed star. How to draw it in one broken line is seen from the figure.
How to draw a star using a ruler and protractor
Now we learn how to draw a regular five-pointed star. Of the measuring instruments you will need a ruler and a protractor.
To make a star, you need to draw segments of the same length so that the internal angles between all five vertices of the figure are 36 °. In practice, this is done as follows - an angle of 36 ° is drawn, segments of the same length are measured from its top, and new straight lines are drawn from their end points at an angle of 36 °.
You can also approach the solution of the problem in a slightly different way by drawing an equilateral pentagon with vertex angles of 106 °, and then connecting its opposite angles with segments.
If you comply with all the conditions, you will ultimately get a beautiful five-pointed star. How to draw it in a simpler way, read on.
How to draw a star using a compass and protractor
Now you need a compass and a protractor. Since the circle is 360 °, then in 1/5 of its part it is 72 ° (360: 5 = 72). Getting to the construction.
Draw a circle with a compass. Mark on it the starting point - the top of the star and the middle of the circle. Take the protractor, align its center with the center of the circle, and mark the future points of the vertices of the star every 72 ° along the entire length of the circle .
It remains to connect them straight, and get a beautiful five-pointed star. How to draw it if there is no protractor at hand? You can do without it, from tools you need only a ruler and a compass.
How to draw a star with a compass and ruler
How to draw a five-pointed star with a pair of compasses? Consider option 1.
Draw a circle. We measure its diameter with a ruler. We make simple mathematical operations: we multiply the diameter of the circle by a factor of 0.58779. The result obtained is the required length of the chord (a straight line connecting 2 points of the curved line, and in our case, a circle), with which we can divide the circle into 5 equal parts.
For example, the diameter of the circle is 7 cm. We multiply 7 x 0.58779 = 4.11453, round up to tenths (since drawing a segment of a more accurate length is not possible on paper), we get 4.1 cm. This will be the desired chord length.
It remains to extend and fix the legs of the compass by a given value, and you can make notches on the circumference. When you connect them, you get a five-pointed star.
How to draw a figure in another way? Consider option 2.
First, draw a regular pentagon inscribed in a circle. How to draw a regular five-pointed star based on it is shown in Figure 2.
Draw a circle with a compass. Conventionally, we denote its center as O. Through point O, draw a line — the diameter of our circle. Draw the radius of this circle so that it is perpendicular to the diameter. We denote the point of intersection of the radius with the circle by V. To the left of point O, set aside the half length of the radius of this circle, mark it with point A. From point A, draw a semicircle through point V until it intersects with the diameter line (it is highlighted in red in the figure) and mark it with point B. The length of the segment VB will be the length of the chord, with which the circle is divided into 5 equal parts. It remains only to connect the resulting points in the form of a star.